def test_expand(self):
print 'expand'
print '1d'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=0)
expanded = grammar.expand_kernels(1, [k],
base_kernels='SE',
rules=None)
for k in expanded:
print '\n', k.pretty_print(), '\n'
print '2d'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=0)
expanded = grammar.expand_kernels(2, [k],
base_kernels='SE',
rules=None)
for k in expanded:
print '\n', k.pretty_print(), '\n'
print '3d'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=0)
expanded = grammar.expand_kernels(3, [k],
base_kernels='SE',
rules=None)
for k in expanded:
print '\n', k.pretty_print(), '\n'
print '3d with two SEs'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=0)
expanded = grammar.expand_kernels(3, [k + k.copy()],
base_kernels='SE',
rules=None)
for k in expanded:
print '\n', k.pretty_print(), '\n'
def test_collapse_mult_idempotent(self):
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = k1 * k2
print '\n', k.pretty_print(), '\n'
k = k.collapse_multiplicative_idempotency()
assert (isinstance(k, ff.SqExpKernel)) and (k.dimension == 0)
print '\n', k.pretty_print(), '\n'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = ff.SqExpKernel(dimension=1, lengthscale=2, sf=2)
k3 = k.copy()
k4 = k.copy()
k5 = ff.NoiseKernel(sf=-1)
k6 = ff.ConstKernel(sf=1)
k = k1 * k2 * k3 * k4 * k5 * k5.copy() + k6 + k6.copy()
print '\n', k.pretty_print(), '\n'
k = k.collapse_multiplicative_idempotency()
print '\n', k.pretty_print(), '\n'
k = k1 * k2 * k3 * k4 * k5 * k5.copy() * k6 * k6.copy()
print '\n', k.pretty_print(), '\n'
k = k.collapse_multiplicative_idempotency()
print '\n', k.pretty_print(), '\n'
def test_distribute_products_k(self):
print 'distribute'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = ff.SqExpKernel(dimension=1, lengthscale=2, sf=2)
k3 = k.copy()
k4 = k.copy()
k5 = ff.NoiseKernel(sf=-1)
k6 = ff.ConstKernel(sf=1)
k = (k1 + k2 + k3) * (k4 + k5)
print '\n', k.pretty_print(), '\n'
components = k.distribute_products().simplified()
print components
print components.collapse_additive_idempotency()
for k in components.operands:
print '\n', k.pretty_print(), '\n'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = ff.SqExpKernel(dimension=1, lengthscale=2, sf=2)
k3 = k.copy()
k4 = k.copy()
k5 = ff.NoiseKernel(sf=-1)
k6 = ff.ConstKernel(sf=1)
k = (k1 * (k2 + k3)) + (k4 * k5)
print '\n', k.pretty_print(), '\n'
components = k.distribute_products().simplified()
print components
print components.collapse_additive_idempotency()
for k in components.operands:
print '\n', k.pretty_print(), '\n'
def test_simplify(self):
m = ff.GPModel(mean=ff.MeanZero(),
kernel=ff.SumKernel(operands=[
ff.ProductKernel(operands=[
ff.ConstKernel(sf=0.170186999131),
ff.SqExpKernel(dimension=0,
lengthscale=1.02215322228,
sf=5.9042619611)
]),
ff.ProductKernel(operands=[
ff.NoiseKernel(sf=2.43188502201),
ff.ConstKernel(sf=-0.368638271154)
]),
ff.ProductKernel(operands=[
ff.NoiseKernel(sf=1.47110516981),
ff.PeriodicKernel(dimension=0,
lengthscale=-1.19651800365,
period=0.550394248167,
sf=0.131044872864)
]),
ff.ProductKernel(operands=[
ff.SqExpKernel(dimension=0,
lengthscale=3.33346140605,
sf=3.7579461353),
ff.PeriodicKernel(dimension=0,
lengthscale=0.669624964607,
period=0.00216264543496,
sf=2.41995024965)
])
]),
likelihood=ff.LikGauss(sf=-np.inf),
nll=599.59757993,
ndata=144)
assert not m.simplified() == m
m = ff.GPModel(mean=ff.MeanZero(),
kernel=ff.SumKernel(operands=[
ff.ProductKernel(operands=[
ff.ConstKernel(sf=0.170186999131),
ff.SqExpKernel(dimension=0,
lengthscale=1.02215322228,
sf=5.9042619611)
]),
ff.ProductKernel(operands=[
ff.NoiseKernel(sf=2.43188502201),
ff.ConstKernel(sf=-0.368638271154)
])
]),
likelihood=ff.LikGauss(sf=-np.inf),
nll=599.59757993,
ndata=144)
assert not m.simplified() == m
def test_canonical_k(self):
print 'canonical_k form'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = ff.SqExpKernel(dimension=1, lengthscale=2, sf=2)
k3 = k.copy()
k4 = k.copy()
k5 = ff.NoiseKernel(sf=-1)
k6 = ff.ConstKernel(sf=1)
k = k1 * k2 * k3 * k4 * k5 * k5.copy() + k6 + k6.copy(
) + k1.copy() * k1.copy() * k3.copy()
print '\n', k.pretty_print(), '\n'
print '\n', k.canonical().pretty_print(), '\n'
def test_additive_form_k(self):
print 'additive form'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = ff.SqExpKernel(dimension=1, lengthscale=2, sf=2)
k3 = k.copy()
k4 = k.copy()
k5 = ff.NoiseKernel(sf=-1)
k6 = ff.ConstKernel(sf=1)
k = (k1 * (k2 + k3)) + (k4 * k5)
print '\n', k.pretty_print(), '\n'
components = k.additive_form().simplified()
print components
for k in components.operands:
print '\n', k.pretty_print(), '\n'
def removeKernelParams(kernel):
"""
Remove hyperparameters of a GPSS kernel and reset them to None.
:returns: a GPSS kernel without parameter initialisation
"""
assert isinstance(
kernel, ff.Kernel), "kernel must be of type flexible_function.Kernel"
if isinstance(kernel, ff.SqExpKernel):
return ff.SqExpKernel(dimension=kernel.dimension)
elif isinstance(kernel, ff.PeriodicKernel):
return ff.PeriodicKernel(dimension=kernel.dimension)
elif isinstance(kernel, ff.ConstKernel):
return ff.ConstKernel()
elif isinstance(kernel, ff.SumKernel):
return ff.SumKernel(map(removeKernelParams, kernel.operands))
elif isinstance(kernel, ff.ProductKernel):
return ff.ProductKernel(map(removeKernelParams, kernel.operands))
elif isinstance(kernel, ff.NoneKernel):
return kernel
else:
raise NotImplementedError("Unrecognised kernel type " +
type(kernel).__name__)
def test_nan_score(self):
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=0)
m1 = ff.GPModel(kernel=k, nll=np.nan, ndata=100)
m2 = ff.GPModel(kernel=k.copy(), nll=0, ndata=100)
(not_nan, eq_nan) = experiment.remove_nan_scored_models([m1, m2],
score='bic')
assert (len(not_nan) == 1) and (len(eq_nan) == 1)
def test_expand_model(self):
print 'expand model'
print '2d'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=0)
m = ff.GPModel(mean=ff.MeanZero(), kernel=k, likelihood=ff.LikGauss())
expanded = grammar.expand_models(2, [m], base_kernels='SE', rules=None)
for k in expanded:
print '\n', k.pretty_print(), '\n'
def test_repr(self):
m = ff.MeanZero()
k = ff.SqExpKernel()
l = ff.LikGauss()
regression_model = ff.GPModel(mean=m, kernel=k, likelihood=l)
print regression_model
print ff.repr_to_model(regression_model.__repr__())
assert regression_model == ff.repr_to_model(
regression_model.__repr__())
def test_collapse_identity(self):
print 'collapse identity'
k1 = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k2 = ff.ConstKernel(sf=-1)
k = k1 * k2
print '\n', k.pretty_print(), '\n'
k = k.collapse_multiplicative_identity()
assert isinstance(k, ff.SqExpKernel)
print '\n', k.pretty_print(), '\n'
k1 = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k = (k1 + k1.copy() + k1.copy() * k2.copy()) * k2
print(k1 + k1.copy()).sf
print(k1.copy() * k2.copy()).sf
print(k1 + k1.copy() + k1.copy() * k2.copy()).sf
print k.sf
print '\n', k.pretty_print(), '\n'
k = k.collapse_multiplicative_identity()
print '\n', k.pretty_print(), '\n'
def test_simplified_k(self):
print 'simplified_k'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = k1 * k2
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k = ff.SqExpKernel(dimension=1, lengthscale=2, sf=2)
k3 = k.copy()
k4 = k.copy()
k5 = ff.NoiseKernel(sf=-1)
k6 = ff.ConstKernel(sf=1)
k = k1 * k2 * k3 * k4 * k5 * k5.copy() + k6 + k6.copy(
) + k1.copy() * k1.copy() * k3.copy()
print '\n', k.pretty_print(), '\n'
k = k.simplified()
print '\n', k.pretty_print(), '\n'
def test_jitter(self):
print 'jitter'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
print[k, k1, k2]
assert (k == k1) and (k == k2) and (k1 == k2)
ff.add_jitter_k([k1, k2])
assert (not k == k1) and (not k == k2) and (not k1 == k2)
print[k, k1, k2]
def test_hash_and_cmp(self):
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
k3 = ff.SqExpKernel(dimension=1, lengthscale=0, sf=1)
assert sorted(list(set([k1, k2, k3]))) == sorted([k1, k3])
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k4 = k.copy()
k5 = ff.NoneKernel()
k6 = ff.ChangePointKernel(operands=[k4, k5])
k7 = ff.ChangePointKernel(
operands=[ff.ChangePointKernel(operands=[k4, k5]), k1])
assert sorted([k1, k2, k3, k4, k5, k6,
k7]) == sorted([k7, k1, k6, k2, k5, k3, k4])
assert sorted(k.canonical()
for k in [k1, k2, k3, k4, k5, k6, k7]) == sorted(
k.canonical() for k in [k7, k1, k6, k2, k5, k3, k4])
assert sorted(k.additive_form()
for k in [k1, k2, k3, k4, k5, k6, k7]) == sorted(
k.additive_form()
for k in [k7, k1, k6, k2, k5, k3, k4])
def test_jitter_model(self):
print 'jitter model'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = k.copy()
print[k, k1, k2]
assert (k == k1) and (k == k2) and (k1 == k2)
m1 = ff.GPModel(kernel=k1)
m2 = ff.GPModel(kernel=k2)
ff.add_jitter([m1, m2])
assert (not k == k1) and (not k == k2) and (not k1 == k2)
print[k, k1, k2]
def test_collapse_add_idempotent(self):
k = ff.SqExpKernel()
k1 = k.copy()
k2 = k.copy()
k = ff.NoiseKernel(sf=-1)
k3 = k.copy()
k4 = k.copy()
k = ff.ConstKernel(sf=1)
k5 = k.copy()
k6 = k.copy()
k = k1 + k2 + k3 + k4 + k5 + k6
print '\n', k.pretty_print(), '\n'
k = k.collapse_additive_idempotency()
print '\n', k.pretty_print(), '\n'
def test_prod(self):
k = ff.SqExpKernel()
k1 = k.copy()
k2 = k.copy()
k = k1 * k2
print '\n', k.pretty_print(), '\n'
print '\n', k.syntax, '\n'
print '\n', k, '\n'
k.operands[0].dimension = 0
k.operands[1].dimension = 1
print '\n', k.pretty_print(), '\n'
print '\n', k.syntax, '\n'
print '\n', k, '\n'
print '\n', k.get_gpml_expression(dimensions=3), '\n'
k.initialise_params(data_shape={
'y_sd': 0,
'x_sd': [0, 2],
'x_min': [-10, -100],
'x_max': [10, 100]
})
print '\n', k, '\n'
assert k == k.copy()
k = k.copy()
print '\n', k, '\n'
assert k == k.copy()
k.load_param_vector(k.param_vector)
print '\n', k, '\n'
k = k + k.copy()
print '\n', k.pretty_print(), '\n'
print '\n', k.syntax, '\n'
print '\n', k, '\n'
print '\n', k.pretty_print(), '\n'
print '\n', k.syntax, '\n'
print '\n', k, '\n'
print '\n', k.get_gpml_expression(dimensions=3), '\n'
k.initialise_params(data_shape={
'y_sd': 0,
'x_sd': [0, 2],
'x_min': [-10, -100],
'x_max': [10, 100]
})
print '\n', k, '\n'
assert k == k.copy()
k = k.copy()
print '\n', k, '\n'
assert k == k.copy()
k.load_param_vector(k.param_vector)
print '\n', k, '\n'
k.sf
def test_model(self):
print 'model'
m = ff.MeanZero()
k = ff.SqExpKernel()
l = ff.LikGauss()
regression_model = ff.GPModel(mean=m,
kernel=k,
likelihood=l,
nll=0,
ndata=100)
print '\n', regression_model.pretty_print(), '\n'
print '\n', regression_model.__repr__(), '\n'
print regression_model.bic
print regression_model.aic
print regression_model.pl2
print ff.GPModel.score(regression_model, criterion='nll')
def test_canonical_k_2(self):
print 'canonical_k form 2'
k = ff.SqExpKernel(dimension=0, lengthscale=0, sf=1)
k1 = k.copy()
k2 = ff.NoneKernel()
k = ff.ChangePointKernel(operands=[k1, k2])
print '\n', k, '\n'
k = k.canonical()
print '\n', k, '\n'
assert k == k1
k = ff.ChangePointKernel(
operands=[ff.ChangePointKernel(operands=[k1, k2]), k2])
print '\n', k, '\n'
k = k.canonical()
print '\n', k, '\n'
assert k == k1
def gpy2gpss(kernel):
"""
Convert a GPy kernel to a GPSS kernel recursively.
Support only:
1) 1-D squared exponential kernels
2) 1-D periodic kernels
3) constant kernels (called `bias` in GPy)
4) sum kernels
5) product kernels
:param kernel: a GPSS kernel as defined in flexible_function.py
:returns: an object of type GPy.kern.Kern
"""
assert isinstance(kernel,
GPy.kern.Kern), "kernel must be of type GPy.kern.Kern"
if isinstance(kernel, GPy.kern.RBF):
sf = np.sqrt(kernel.variance)[0]
ls = kernel.lengthscale[0]
dim = kernel.active_dims[0]
return ff.SqExpKernel(dimension=dim, lengthscale=ls, sf=sf)
elif isinstance(kernel, GPy.kern.StdPeriodic):
sf = np.sqrt(kernel.variance)[0]
ls = kernel.lengthscale[0]
per = kernel.period[0]
dim = kernel.active_dims[0]
return ff.PeriodicKernel(dimension=dim,
lengthscale=ls,
period=per,
sf=sf)
elif isinstance(kernel, GPy.kern.Bias):
sf = np.sqrt(kernel.variance)[0]
return ff.ConstKernel(sf=sf)
elif isinstance(kernel, GPy.kern.Add):
return ff.SumKernel(map(gpy2gpss, kernel.parts))
elif isinstance(kernel, GPy.kern.Prod):
return ff.ProductKernel(map(gpy2gpss, kernel.parts))
else:
raise NotImplementedError("Cannot translate kernel of type " +
type(kernel).__name__)
def test_restarts(self):
print 'restart'
data_shape = {
'y_sd': 0,
'x_sd': [0, 2],
'x_min': [-10, -100],
'x_max': [10, 100]
}
k = ff.SqExpKernel(dimension=0)
k1 = k.copy()
k2 = k.copy()
print[k, k1, k2]
assert (k == k1) and (k == k2) and (k1 == k2)
kernel_list = ff.add_random_restarts_k([k1, k2],
data_shape=data_shape,
sd=1)
k1 = kernel_list[0]
k2 = kernel_list[1]
assert (not k == k1) and (not k == k2) and (not k1 == k2)
print[k, k1, k2]
def test_restarts_model(self):
print 'restart model'
data_shape = {
'y_sd': 0,
'x_sd': [0, 2],
'x_min': [-10, -100],
'x_max': [10, 100]
}
k = ff.SqExpKernel(dimension=0)
k1 = k.copy()
k2 = k.copy()
print[k, k1, k2]
assert (k == k1) and (k == k2) and (k1 == k2)
m1 = ff.GPModel(kernel=k1)
m2 = ff.GPModel(kernel=k2)
model_list = ff.add_random_restarts([m1, m2],
n_rand=1,
data_shape=data_shape,
sd=1)
k1 = model_list[0].kernel
k2 = model_list[1].kernel
assert (not k == k1) and (not k == k2) and (not k1 == k2)
print[k, k1, k2]
